The analysis of dispositions is used to consider cases where the effect of one
disposition operating is the existence of another disposition. This may arise
from rearrangements within aggregated structures of dispositional parts, or, it
is argued, also as stages of derivative dispositions within a set of multiple
generative levels. Inspection of examples in both classical and quantum physics
suggests a general principle of `Conditional Forward Causation': that
dispositions act 'forwards' in a way conditional on certain circumstances or
occasions already existing at the `later' levels.

Recently, the much philosophical work has emphasized the importance of
dispositions for realistic analyses of causal processes in both physics and
psychology. This is partly because of the attractiveness of the thesis of
dispositional essentialism, which holds that all existing things have irreducible
causal powers, and such views are advocated in Bird [2004], Cartwright [1989],
Chakravartty [2003], Elder [1994], Ellis [2000,2001], Ellis and Lierse [1994],
Fetzer [1977], Harré and Madden [1975], McKitrick [2003], Molnar [2004],
Mumford [1995, 1998], Shoemaker [1984], Swoyer [1982] and Thompson [1988]. The
thesis opposes the views of Ryle [1949] who sees dispositions as merely
`inference tickets' or `promises', and Armstrong [1969] who sees them as
derived from universal laws combined with nondispositional properties. Mumford
[2005] articulates a common aspect of dispositional essentialism, to imagine
how the concept of universal laws could be rather replaced by talk of
specific objects and their dispositions.

Recent critics of dispositional essentialism have pointed, for example, at
Least Action Principles (Katzav [2004]), and Gauge Invariance Principles
(Psillos [2005]), both of which principles appear to be independent laws that
do not follow the pattern of aggregations with dispositions of the
constituents. It might therefore appear that we have to move our understanding
beyond that of simple dispositions. Related complexities are described in the
works of Krause [2005] and Stachel [2005], who consider the difficulties
arising from the identity of indistinguishable particles in quantum mechanics.

It may well be that concepts of more sophisticated kinds of dispositions
allow us to make headway in understanding the
above complications within the framework of dispositional essentialism.
I therefore continue the analysis of kinds of dispositions, to consider the
possibility of derivative dispositions, and later consider whether
these together may form a structure of multiple generative levels. This
paper therefore consists of proposals for what those concepts might mean, and
of analyses of examples in physics and psychology that appear to need such
concepts for their understanding. We need to distinguish the cases whereby
new dispositions come about from rearrangement of parts, from possible
cases where they are `derived' or `generated' in some more original way.

Most examples of dispositions in philosophical discussions are those, like
fragility, solubility, radioactive instability, whose effects (if manifested)
are events. If a glass exercises its fragility, it breaks. If salt shows
its solubility, it dissolves, and the manifestation of radioactive instability
would be a decay event detected say with a geiger counter. However, physicists
want to know not merely that these events occur, but also how the
dispositions themselves may change after the manifestation event. In the
cases here, the fragility of the parts or the stability of the nuclei may
change as results of the manifestation events, and it is still part of physics
to describe the new (changed) dispositions as accurately as possible. Such
descriptions are part of dynamical accounts, as distinct from descriptive
accounts events.

Sometimes, new dispositions may be ascribable after an event which could
not be done so before an event. The fragments of a broken glass may be able to
refract light in a way that the intact glass could not, for example. The
dissolved salt may be to pass through a membrane, in contrast to the
dispositions of the initial salt crystals. The fragments of nuclear decay may possibly
decay by emitting electrons in a way the parent nucleus could not.

In general, it appears often that new dispositions may be truthfully ascribed as
the result of the operation of a prior disposition.
If the ascription of dispositions is attributed to the existence properties of some object,
then it appears that, in the above examples, new dispositions come into existence
as the manifestation of previous dispositions. Since now one disposition leads
to another, some philosophical analysis is called for.

The existence of some of these new dispositions may perhaps be successfully
explained as the rearrangement of the internal structures of the objects under
discussion, which are then presumably composite objects. The refraction by
pieces of broken glass, in contrast to the original smooth glass, has obvious
explanations in terms of the shapes of the new fragments. Salt's
diffusion through a membrane, once dissolved, is presumably because of the
greater mobility of salt ions in solution compared with the crystal form.

Science is largely successful in explaining such dynamical evolutions of
empirical dispositions of natural objects. It bases the explanations in terms
of changes in their structural shapes and arrangements of their parts, along
with the fixed underlying dispositions or propensities of these parts. It is
from the dispositions of these parts that, according the structure, all their
observed dispositions and causal properties may be explained.

The existence of new dispositions by rearrangement of the parts of an object,
I take to be non-controversial within existing philosophical frameworks.
It appears that typical philosophical analyses need only slight modifications to
take into account the way the derivative dispositions of an aggregate are explained in terms of
recombinations of the dispositions of its parts.

However, it also appears that not all dynamical changes of dispositions occur
by rearrangements of parts, and these are what in this paper I want to call
derivative dispositions. There are some cases, to be listed below, where
new dispositions come into existence, without there being any visible parts
whose rearrangement could explain the changes. The next section gives some
examples of what appear to be such derivative dispositions, and this is
followed by a more general analysis of how these might work.

If there turns out to be a sequence of derivative dispositions, then the
combined structure may be said to be that of `multiple generative levels'. We
will see some examples below.

If we look at physics, and at what physics regards as part of its central
understanding, one extremely important idea is energy.
Physics talks about kinetic energy as energy to do with motion, and
potential energy as to do with what would happen if the circumstances
were right. More specifically, if we look at definitions of force and energy
which are commonly used to introduce these concepts, we find definitions like

force: the tendency F to accelerate a mass m with acceleration F/m.

energy: the capacity E to do work,
which is the action of a force F over a distance d,

potential energy field: the field potential V(x) to exert a force F = -dV/dx
if a test particle is present.

As Cartwright [1989] points out, force is not identical to the product ma,
because it is only the net force at a point which is important. An
individual force is only by itself a tendency which may or may not be
manifested. It is a disposition, as is energy generically, as well as potential
energy. Furthermore, we may see a pattern here:

potential energy field: the disposition to generate a force, and

force: the disposition to accelerate a mass, and

acceleration: the final result.

I take this to be an example of two successive derivative dispositions,
where the effect of one disposition operating is the generation of another. An
electrostatic field potential is a disposition, for example, the manifestation
of which is not itself motion, but which is the presence now of a derivative
disposition, namely a force. The manifestation of a force may or may not occur
as motion, as it depends on what other forces are also operating on the mass.
The production of a force by a field potential does not appear to be something
that occurs by means of the rearrangements of microscopic parts, but appears to
be more fundamental, and almost sui generis. It is clearly in need of
philosophical inspection, as it appears that field potentials,
force and action form a set of multiple generative levels.

Admittedly, many physicists and philosophers often manifest here a tendency to
say that only potential energy is `real', or conversely perhaps that
`only forces are real', or even that `only motion is real', and that in each
case the other physical quantities are only `calculational devices' for
predicting whichever is declared to be real. Please for a while apply a
contrary tendency to resist this conclusion, at least to the end of the paper.
In §5 I will be explicitly evaluating such `reductionist
strategies, along with the comparative roles of mathematical laws and
dispositional properties within a possible dispositional essentialism.

In quantum physics, energy (the total of the kinetic and potential energies) is
represented by the Hamiltonian operator . This operator enters into
the Schrödinger wave equation
, which governs all quantum wave forms . It
thus generates all time evolution, and hence all fields of probabilities
for measurement outcomes. The principal dynamics in quantum
physics are specified by knowing what the initial state is, and what the
Hamiltonian operator is. These remarks apply to quantum mechanics as it is
practised, by using Born's statistical interpretation and then naively saying
that the quantum state changes after a measurement to one of the eigenstates of
the measurement operator. This is the much discussed `reduction of the wave
packet', which we agree at least appears to occur.

We may therefore consider quantum physics in the following `realistic' way. We
have the Hamiltonian which is to do with total energy, which is somehow
`active' since it is an operator which operates on the wave function and
changes it. The Schrödinger equation is the rule for how the Hamiltonian
operator produces the a wave function, which is a probabilistic disposition (a
propensity) for action. This wave function (in fact its squared modulus) gives
a probability for different of macroscopic outcomes of experiments, and the
wave function changes according to the specific outcome.

Such is the structure of quantum physics as it is practised, and we may observe
derivative dispositions in operation:

Hamiltonian operator: the fixed disposition to
generate the wave function by evolving it in time,

It appears again that we have multiple generative levels, with the set of
Hamiltonian, wave function and selection event. Note here
also that the final result is not a disposition, but the last of a sequence of
derivative dispositions. For completeness, therefore, we include such a `bottom
line' within the concept of multiple generative levels.

Admittedly again, reductionist tendencies may be applied. Most commonly, it may
be denied that there are distinct measurement outcomes in any ontological
sense, and that they may only be approximately defined within a coarse-grained
`decoherent history'. Advocates of the Many Worlds Interpretation, or of
Decoherence theories, take this view. Others such as Bohr take the opposite
view! Bohr holds that only the measurement outcome is real, and that the
Hamiltonian and wave function are calculational devices and nothing real. These
views in tension will be discussed in §5.

Taking a broader view of contemporary physics and its frontiers, we may say
that the `Hamiltonians, wave functions and measurements' of above describe just
the dispositions for a class of `actual processes'. The Hamiltonian is the
operator for the total energy, containing both kinetic and potential energy
terms. However, we know from Quantum Field Theory (QFT) that, for example, the
Coulomb potential is composed `in some way' by the exchange of virtual photons.
Similarly, we also know from QFT that the mass in the kinetic energy part is
not a `bare mass', but is a `dressed mass' arising (in some way) also from many
virtual processes. This again suggests the theme of my paper: that the
Hamiltonian is not a `simple disposition', but in fact is itself
derivative from some prior `generative level'. In this case the needed
generative level could be called that of `virtual processes', in contrast to
that of `actual processes'.

The class of virtual processes, as described by QFT, have many properties that
are opposite to those of actual selections of measurement outcomes. Virtual
events are at points (not selections between macroscopic alternatives), are
interactions (not selections), are continuous (not discrete), are deterministic
(not probabilistic), and have intrinsic group structures (e.g. gauge
invariance, renormalisation) as distinct from the branching tree structure of
actual outcomes. All these contrasts (which I do not have the space to expound
here) suggest that virtual processes should be distinguished from actual
events. The guiding principles have different forms. Virtual processes are most
commonly described by a Lagrangian subject to a variational principle in a Fock
space of variable particle numbers, whereas actual processes, as discussed
above, deal with the energies of specific observable objects leading to
definite measurement outcomes.

Field theories still use a geometric background of spacetime, and there is
currently much speculative work in quantum gravity research to determine how
this spacetime might arise. Wheeler started interest in `pregeometry': the
attempt to formulate theories of causal processes which do not presuppose
a differentiable manifold for spacetime. Rather, the aim to speculate how
spacetime might arise. Most commonly, the task has been taken as showing how
spacetime may turn out to be a `statistical approximation' in some limit of
large numbers of hypothetical pregeometric processes. Proposals have involved
spinors by Penrose [1987], `loop quantum gravity' as described for example in
Rovelli [1998], and `causal sets' according to Brightwell and Dowker [2003].

If some pregeometry could be identified, I could speculate that a good way of
seeing this would be as a distinct pregeometric level with a structure of
derivative dispositions. That is, instead of spacetime being a statistical
approximation (in the way thermodynamics is a statistical approximation to
molecular gas theories), it could be better imagined that spacetime is an
aspect of derivative dispositions that have been generated by `prior'
pregeometric dispositions. This is admittedly very speculative, but it does
follow the pattern of some current research, so I use it as an example of how
the philosophical analysis of dispositions may yet interact fruitfully with
modern physics. This appears to be useful particularly since the very aim of
`deriving spacetime' has itself been called into question by Meschini et al. [2004].

There are many examples of apparent derivative dispositions in everyday life,
in psychology, in particular in cognitive processes. These dispositions are
involved whenever the accomplishment of a given disposition requires the
operation of successive steps of kinds different from the overall step. The
original disposition on its operation therefore generates the
`derived dispositions' for the intermediate steps, which are means to the
original end. An original `disposition to learn', for example, can generate the
derived `disposition to read books', which can generate further `dispositions
to search for books'. These dispositions would then generate dispositions to
move one's body, which in turn lead ultimately to one's limbs having (physical)
dispositions to move. These successively generated dispositions are all
derived from the original disposition to learn, according to the specific
situations.

Another example of sequential and derivative dispositions is the ability to learn. To
say that someone is easy to teach, or that they are musical, for example, does
not mean that there is any specific action that they are capable of doing.
Rather, it means that they well disposed to learn new skills (whether of a
musical or of a general kind), and that it is these new skills which are the dispositions
that lead to specific actions.

In this I follow Broad [1925]: that there are `levels' of causal influence. We
might allow that particular dispositions or intentions are best regarded not as
the most fundamental causes, but as `intermediate stages' in the operation of
more persistent `desires' and `motivations'. The intention to find a book, for
example, could be the product or derivative of some more persistent `desire for
reading', and need only be produced in the appropriate circumstances. Broad
would say that the derived dispositions were the realisation of the
underlying dispositions.

The first general idea is that `multiple generative levels' are a sequence {A
B C .. } in which A `generates' or `produces' new forms of B
using the present form of B as a precondition. We say that B derives from A as
its manifestation. Then B generates C in the same way. This sequence may
perhaps continue until an end Z, say, where nothing is active.

This rough scheme does not tell us, however, how A, B, etc might be
changed as a result of their operation. Presumably this occurs often, as
for example in naive quantum theory, when a wave function is changed after it
generates a particular measurement outcome. We want to consider the possibility
of a general scheme which might explain the (apparently mysterious) logic of
the `reduction of the wave packet'. In order to formulate a general scheme, let
us extract some guidelines from our example derivative dispositions listed
previously. To do this, we will need to first distinguish the concepts of principal from
instrumental and occasional causes.

Davidson [1967] argues that causality is a two-place relation between
individual events. Thus causal relations are certainly not just implications
from the description of the first event to that of the second event, but are
something more real. The reality of causality, however, does not thereby
automatically include such components as dispositions and propensities,
although Steiner [1986] wants to extend Davidson's ideas in this direction. I
want to allow both dispositions and previous events to be causes,
although in different senses.

Distinctions thus ought to be made between

the `Principal Cause': that disposition which operates,

the `Occasional Cause': that circumstance according to which dispositions operate,

the `Instrumental Cause': the origin of the occasional cause, so is
another cause by means of which the Principal Cause operates.

The overall pattern is therefore that ``Principal causes operate according to
occasional causes, which arise from instrumental causes''.

All three kinds of causes appear to be necessary for any event in nature, for
example, when a stone is let fall: the principal cause is the earth's
gravitational attraction, the occasional cause is our act of letting go, and
instrumental cause is the muscle movements in our finger releasing the stone.
Its hitting the ground is thus caused by our letting go, but only as an
instrumental and then occasional cause. Many common uses of `cause' (including
that of Davidson [1967]) refer to occasional causes rather than principal
causes, as it is only in the occasional sense that events can be said to
be causes. Previous events cannot be efficacious causes, Emmet [1984] points
out, in the sense of `producing' or `giving rise to' their effects. The
instrumental cause is a genuine causal contributor, and may be said to `set the
stage', by making suitable conditions (namely, the occasional cause) for the
operation of the principal cause.

Consider now a electron of fixed charge and mass moving in an electrostatic
potential, according to classical electrostatics. At a given place x, the
derivative of the potential V(x) gives the force, and the force gives
acceleration which in turn changes the velocity of electron, and it moves to a
new place. In our framework of derivative dispositions, we see that the
potential is a disposition which generates another, namely the force. It does
so, moreover, according to the place of the electron. The electrostatic
potential is therefore the principal cause of the force, and the place of the
electron is the occasional cause. A place by itself is never an efficacious
cause, but it can be said to be the circumstance by means of which the
potential generates the force. Note that we never have forces causing
potentials to exist where they did not before, nor are places themselves
dispositional. Let us generalise by surmising a set of generative levels
{Potential Force Places}, such that the principal causation is
always in the direction of the arrow, and the only apparent `backward'
causation is with the occasional cause. The only feedback `back up the
sequence' is with the conditional aspect of certain occasions, and how the
operation of prior dispositions somehow still depends on particular occasions
as preconditions.

Consider also the quantum mechanical evolution of a system from time t0 that
is subject to measurement selections at various later times t1, t2, etc.
The quantum mechanical story is as follows. The initial quantum state
is evolved according to the Schrödinger equation by the
Hamiltonian for t < t1. Consider the measurement for operator
occurring at t = t1, the operator having an eigenexpansion
. In practical quantum mechanics, the
quantum state changes to
if the result of the
measurement is the eigenvalue , which occurs with probability
. The new state
is then evolved similarly for t < t2, the time of the next
measurement.

Seen in terms of derivative dispositions, the Hamiltonian is the disposition to
evolve an initial state to new times t, generating
. The new are themselves another
disposition, namely a propensity to produce measurement outcomes with the
various probabilities
. The
final results are the discrete selection events at the times of measurement.
These discrete events have themselves no causal power, but definitely influence
the future evolutions of the wave function. In that sense, they are `occasional
causes' according to which other dispositions may operate. The principal
dispositions are first the Hamiltonian operator that starts the whole process,
and then the wave functions considered as fields of propensity for different
selection events. Summarising the quantum mechanical case, we see that here
again, the principal causes act `forwards' down a set of multiple generative
levels, yet act conditionally on certain events. These events thereby become
occasional causes. Because the wave functions before a measurement event are
the cause of that event, those wave functions are thereby the instrumental
cause of the new wave functions after the measurement.

From our examples, we may generalise that all the principal causation is `down'
the sequence of multiple generative levels {A B ... }, and that
the only effect back up the sequence is the somehow the way principal causes
still depend on certain occasions in order to operate. Let us adopt as
universal this asymmetric relationship between multiple generative levels: that
dispositions act forwards in a way conditional on certain things already
existing at the later levels. We regard this as a simple initial hypothesis,
and will have to observe whether all dispositions taken as existing in nature follow
this pattern.

We may therefore surmise that A, the first in the sequence, is the `deepest
underlying principle', `source', or `power' that is fixed through all the
subsequent changes to B, C, etc. Conditional Forward Causation, the pattern we
saw from physics, would imply that changes to B, for example, come from
subsequent operations of A, and not from C, D,.. acting in `reverse' up the
chain. Rather, the subsequent operations of A are now conditioned on the
results in B, C, D, etc. The operations of A are therefore the principal
causes, whereas the dependence of those operations on the previous state of B
is via instrumental causation, and the dependence on the results in C,
D,... is via occasional causation. It is now hypothesized that this is a
universal pattern for the operation of dispositions in nature that do not
follow from the rearrangement of parts of an aggegrate object.

5 Reductionism and Dispositional Essentialism

In all the apparent examples of multiple generative levels given here, many
physicists and philosophers of physics will want to assert the particular
`reality' of one of the levels, and say that the prior levels are `merely
calculational devices' for the behaviour of their chosen real level.

For example, some assert in electromagnetic theory that only the field tensors
(incorporating the electric and magnetic vector fields) are `real', and that
the vector potential (incorporating the electrostatic potential) is a
calculational device with no reality. To this end, they note the gauge
uncertainties in the vector potential, which for electrostatics is the
arbitrariness in setting the level of zero potential energy. Against this, many
have noticed that the scattering of electrons in the Bohm-Aharonov experiment
is most succintly explained in terms of the vector potential, not the field
tensor. It turns out that it is loop integrals of the vector potential which
carry physical significance, so there are non-trivial physical and
philosophical questions about the relative `reality' of potentials and forces
which require not immediate preferences but considered responses.

We also saw how reductionist tendencies may be manifest in quantum theories.
`Decoherent history' accounts of quantum mechanics want to keep the wave
function according to the Schrödinger equation, and deny that macroscopic
outcomes occur in a reality, and only allow them to be approximate appearances.
The founders of quantum theory such as Bohr and Wheeler, however, took the
opposite view, that an electron is only `real' when it is being observed -
when it makes the flash of light at a particular place - not while it is
travelling. In this opposite view the Hamiltonian and wave function are
calculational devices and nothing real, having only mathematical reality as
portrayed by the mathematical name `wave function'.

The views which make prior levels into calculational devices can be critiqued
from the point of view of dispositional essentialism. This view encourages us
in general to not invoke arbitrarily mathematical rules for the laws of
nature, but, as Mumford [2005] suggests, replace the role of laws by that
of the dispositional properties of particular objects. The question of
simplicity, to be answered in order to apply Occam's criterion, is therefore
whether it is simpler to have multiple kinds of objects existing (even within
multiple generative levels) each with simple dispositions, or simpler to have fewer
kinds of existing objects, but with more complicated laws governing their
operation. The discussion in the literature about interpreting the
Bohm-Aharonov effect is trying to answer precisely this question, once it had
been established that different approaches were both adequate in explaining the
phenomenon.

In the present paper, I have shown many more apparent examples of multiple
generative levels, composed of derivative dispositions. The questions of
simplicity, and adequacy, will have to be examined now in all of these cases as
well.